Nonlocal transport models for capturing solute transport in one‐dimensional sand columns: Model review, applicability, limitations and improvement

Abstract

Modelling pollutant transport in water is one of the core tasks of computational hydrology, and various physical models including especially the widely used nonlocal transport models have been developed and applied in the last three decades. No studies, however, have been conducted to systematically assess the applicability, limitations and improvement of these nonlocal transport models. To fill this knowledge gap, this study reviewed, tested and improved the state-of-the-art nonlocal transport models, including their physical background, mathematical formula and especially the capability to quantify conservative tracers moving in one-dimensional sand columns, which represents perhaps the simplest real-world application. Applications showed that, surprisingly, neither the popular time-nonlocal transport models (including the multi-rate mass transfer model, the continuous time random walk framework and the time fractional advection-dispersion equation), nor the spatiotemporally nonlocal transport model (ST-fADE) can accurately fit passive tracers moving through a 15-m-long heterogeneous sand column documented in literature, if a constant dispersion coefficient or dispersivity is used. This is because pollutant transport in heterogeneous media can be scale-dependent (represented by a dispersion coefficient or dispersivity increasing with spatiotemporal scales), non-Fickian (where plume variance increases nonlinearly in time) and/or pre-asymptotic (with transition between non-Fickian and Fickian transport). These different properties cannot be simultaneously and accurately modelled by any of the transport models reviewed by this study. To bypass this limitation, five possible corrections were proposed, and two of them were tested successfully, including a time fractional and space Hausdorff fractal model which minimizes the scaledependency of the dispersion coefficient in the non-Euclidean space, and a two-region time fractional advection-dispersion equation which accounts for the spatial mixing of solute particles from different mobile domains. Therefore, more efforts are still needed to accurately model transport in non-ideal porous media, and the five model corrections proposed by this study may shed light on these indispensable modelling efforts.

General Backward Model to Identify the Source for Contaminants Undergoing Non-Fickian Diffusion in Water

“…Model (1) may be a general unifying model where the same parameters may reflect different diffusive processes (driven by different mechanisms) in different hydrologic systems (such as surface water versus subsurface water). Theoretical justifications for the space-dependent transport parameters in almost all of the state-of-the-art, nonlocal transport models were articulated in Zhang et al We will also test these hypotheses in Section . It is also noteworthy that eq can be obtained by adding the subdiffusive term to the space fADE proposed by Zhang et al A detailed derivation of this equation is also shown in Section S.1.4.…”

Influence of Clay on Solute Transport in Saturated Homogeneous Mixed Media

“…This means that CTRW places more emphasis on the transition time distribution than the transition length since the residence times of fluids and solutes quantify transport in porous media. In this study, the concept of CTRW is summarised and the detail of the importance of waiting time distribution, which the CTRW model is all about, is documented in the publications [7,43].…”

Time‐Fractional Flow Equations (t‐FFEs) to Upscale Transient Groundwater Flow Characterized by Temporally Non‐Darcian Flow Due to Medium Heterogeneity

“…Although these parameters have clear physical meanings, they cannot be measured directly at present and must be fitted. The same limitation (i.e., poor parameter predictability) persists for most nonlocal, upscaling transport models (Zhang et al, 2020). Empirical approximation of model parameters will be discussed in Section 5.4.…”